Approximation of the mixed additive and cubic functional equation in paranormed spaces.

In this paper, we prove some theorems about the Hyers-Ulam stability of the functional equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 2[f(2x) - 2f(x)] in paranormed spaces. From these theorems, as corollaries, we obtain the stability of the above functional equation with weaker conditions controlled by product of powers of norms and mixed-type product-sum of powers of norms. [ABSTRACT FROM AUTHOR]